Lithography in the deep submicron era employs photoresists of very different working principles from the previous generations. Because of the reduced power level of the light sources at the wavelength of Deep Ultra-Violet(DUV), the resists employing the principles of chemical amplifications are developed, and are called the Chemically Amplified Resists(CAR).
As the resist film is exposed to the DUV light, the latent image of photoacids conforming to the photomask patterns is produced in the resist. After exposure, the resist film is baked at elevated temperature for the protection polymers to react with the photoacids, and this process is called the Post-Exposure Bake(PEB).
In the PEB process, the protection polymers in the resist undergo a catalytic reaction with the photoacids, and are gradually annihilated for the case of positive CARs. At the end of the PEB process, the resist in the exposed area is, thus, deprotected, and has a much larger etch rate than in the unexposed area. Namely, as a result of the PEB process, the exposed portions of the photoresist become soluble and can be readily washed away by the developer.
At the elevated temperature of PEB, both the reaction mechanism of protection polymers and photoacids and the diffusion mechanism of photoacids occur. The PEB model which includes the coupling of the two mechanisms was published in the literature and was granted U.S. Pat. 5,717,612 later (See, for example, L. Capodieci, A. Krasnoperova, F. Cerrina, C. Lyons, C. Spence, and K. Early, Novel post-exposure bake simulator: first results,"J. Vac. Sci. Technol., vol. B13, no. 6, pp. 2963-2967, 1995.). However, in the prior art, the reaction and diffusion mechanisms were modeled with fixed reaction constants and diffusion coefficient in the course of the bake process.
Because the reaction constants satisfy Arrhenius type of relations, the reaction rates have strong dependence on temperature. The temperature-time history, in turn, depends on the configurations of the bake apparatus and can be quite different between configurations. Hence, the reaction constants have to be modeled as time-dependent parameters in course of the PEB process.
Furthermore, the diffusion coefficient is reported to be dependent on both temperature and protection-site concentration.
Consequently, to physically model the PEB process, it is necessary to take into account the temperature-dependence and the protection-site-dependence of the reaction constants and the diffusion coefficient, and the temperature-time history of the bake apparatus.